Solving logarithmic equations

The video tutorial explains how to solve a logarithmic equation using the one-to-one property of logarithms. It begins by setting up the equation with natural logarithms and then applies the one-to-one property, which states that if the logarithms of two expressions are equal, the expressions themselves are equal. The tutorial then demonstrates solving the equation by isolating the variable and using inverse operations, ultimately finding the solution. The process is summarized to reinforce understanding.

What is the initial problem presented in the video involving natural logarithms?

• Solving an equation with natural logarithms

• Graphing a logarithmic function

• Integrating a logarithmic function

• Finding the derivative of a logarithmic function

What does the one-to-one property of logarithms state?

• If two logarithms with the same base are equal, their arguments are equal

• Logarithms with different bases can be equated

• Logarithms can be multiplied directly

• Logarithms can be added directly

What is the base of natural logarithms?

• π

• e

• 2

• 10

After applying the one-to-one property, what is the next step in solving the equation?

• Graph the equation

• Use inverse operations to isolate x

• Differentiate the equation

• Integrate the equation

What is the final solution for x in the equation presented?

• x = 7

• x = 6

• x = 8

• x = 5